Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model

2003 ◽  
Vol 73 (5) ◽  
pp. 333-345 ◽  
Author(s):  
Gejza Wimmer ◽  
Viktor Witkovský
Keyword(s):  
Random Effects ◽  
Variance Component ◽  
Interval Estimation ◽  
Random Effects Model

Estimators of Random Effects Variance Components in Meta-Analysis

2000 ◽  
Vol 25 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Lynn Friedman
Keyword(s):  
Closed Form ◽  
Random Effects ◽  
Quadratic Forms ◽  
Relative Efficiency ◽  
Variance Component ◽  
Linear Models ◽  
Random Effect ◽  
Linear Functions ◽  
Effect Sizes ◽  
Random Effects Model

In meta-analyses, groups of study effect sizes often do not fit the model of a single population with only sampling, or estimation, variance differentiating the estimates. If the effect sizes in a group of studies are not homogeneous, a random effects model should be calculated, and a variance component for the random effect estimated. This estimate can be made in several ways, but two closed form estimators are in common use. The comparative efficiency of the two is the focus of this report. We show here that these estimators vary in relative efficiency with the actual size of the random effects model variance component. The latter depends on the study effect sizes. The closed form estimators are linear functions of quadratic forms whose moments can be calculated according to a well-known theorem in linear models. We use this theorem to derive the variances of the estimators, and show that one of them is smaller when the random effects model variance is near zero; however, the variance of the other is smaller when the model variance is larger. This leads to conclusions about their relative efficiency.

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